Not the exact same as the originals or sequels(unless they come after, which would make more sense really to keep everyone up-to-date) but keeping the base of the story intact while reworking it to give it the true depth the originals lacked(my favorite games but I admit that it felt like the story was lacking some things).
I like the idea of giving Norman/your move to Hoenn more of a backstory and the Juan/Wallace connection showing more. It would also be great if the gym leaders, etc. were given more of a role in things(BW + B2W2 really made good use of that) and having them appear out of their gyms from time to time.
There's so many things they can do to breathe more life into the games without needing to make some drastic drastic changes, aside from graphics obviously, and the 3DS could make it happen!
and remember, pretty soon R/S won't even be compatible because of GBA, the newest DS's don't have the GBA slot, and a lot of people ditched the lite for the 3DS or the DSi, which of course don't have one, but as XanderO said, you can get every pokemon in 3rd Gen but people that started with HG/SS or above won't have the chance to play through that story.